Agree with Syntax and Raul. The only thing that resonance frequency calculation will do is prevent a gross mismatch. Otherwise it's a mildly interesting waste of time. (Of course, as Raul said, if that's the kind of thing you enjoy, you'll enjoy it!)
Assuming no gross mismatch, that calculation will tell you nothing about how a cartridge and arm will perform together sonically. Experience with the actual combination is the only way to know that, and Syntax apparently has plenty with the Phantom. Further, I'd surmise that the Phantom's damping facility should make it possible to handle the stray energies eminating from many different cartridges, which is what arm-cartridge matching is actually about.
Oh, how to avoid a "gross mismatch"? Simple. Whatever the Phantom's exact effective mass, it's reasonable to call it "medium". The arm is neither a flyweight nor a beast. So just avoid very light or very heavy cartridges and also avoid very compliant or very non-compliant suspensions. That guarantees you won't have a gross mis-match.
Choose your cartridge based on:
1. your budget,
2. the capabilities of your phono stage,
3. the kind of sound you prefer, and
4. the one that makes you smile when you look at it.
Less fuss, more tunes,
Doug
